I think it's the emphasis that bothers people. Many players when they would say the school names on MNF would say, "The University of Georgia, The University of Florida, etc." However, it was really during Eddie's time, late 90s on, that I remember players emphasizing THE Ohio State University.
Honestly, back then, there was not as big of a backlash against OSU, so people didn't say much, because it just sounded like sour grapes. Now, since the current incarnation of the team and the entire fanbase and student and faculty bodies are held responsible for two subpar (well one really bad, and one somewhat respectable) appearances in the national title game, OSU has become everyone's target.
I am still holding out hope for two SEC teams to make the playoffs and OSU beating them BOTH to win a title. That will shut most people up, or at least make them just look bitter for saying anything.